Question

Given the square root function, y =1/2√x + 3 − 9 , what is the y-value when x=13 ?(1 point) Responses −5 negative 5 −7 negative 7 2 2 −1

Answer 1

To find the y-value when \( x = 13 \) for the function \( y = \frac{1}{2} \sqrt{x} + 3 - 9 \), we can substitute \( x \) with 13:

\[
y = \frac{1}{2} \sqrt{13} + 3 - 9
\]

First, calculate \( \sqrt{13} \):

\[
\sqrt{13} \approx 3.605551
\]

Now substitute this value back into the equation:

\[
y = \frac{1}{2} \times 3.605551 + 3 - 9
\]

Calculating \( \frac{1}{2} \times 3.605551 \):

\[
\frac{1}{2} \times 3.605551 \approx 1.8027755
\]

Now substitute this back into the equation:

\[
y \approx 1.8027755 + 3 - 9
\]

Now, simplify:

\[
y \approx 1.8027755 + 3 = 4.8027755
\]

Then subtract 9:

\[
y \approx 4.8027755 - 9 \approx -4.1972245
\]

Since we're looking for the options:

- negative 5
- negative 7
- 2
- negative 1

The closest value is approximately \(-5\).

Thus, the answer is \(\text{-5}\).